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絕對值 定義

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. Essentially, absolute value turns all negative numbers positive and leaves positive numbers and zero unchanged. The absolute value of a number may be thought of as its distance from zero.

數字的絕對值是數字與origin 之間的距離。這是絕對值的更精確定義，因為它將絕對值的概念與複數的絕對值 和向量的大小 聯繫起來。實數的絕對值的推廣出現在各種各樣的數學設置中。例如，還為複數、四元數、有序環、域和向量空間定義了一個絕對值。絕對值與各種數學和物理上下文中的 magnitude、距離和 norm 的概念密切相關。